Question

a energy does not affect the wavelength of radiation on the electromagnetic spectrum.
b wavelength decreases as energy remains the same across the electromagnetic spectrum.
c wavelength increases as energy increases across the electromagnetic spectrum.
d wavelength decreases as energy increases across the electromagnetic spectrum.

Explanation:

To solve this, we recall the relationship between energy (\(E\)), wavelength (\(\lambda\)), and frequency (\(f\)) of electromagnetic radiation: \(E = hf\) (Planck's equation, where \(h\) is Planck's constant) and \(c = f\lambda\) (where \(c\) is the speed of light). From \(c = f\lambda\), we can express \(f=\frac{c}{\lambda}\). Substituting into Planck's equation gives \(E = h\frac{c}{\lambda}\). This shows that energy (\(E\)) and wavelength (\(\lambda\)) are inversely proportional (since \(h\) and \(c\) are constants). So as energy increases, wavelength decreases, and vice versa.

• Option A: Incorrect, as energy and wavelength are related.
• Option B: Incorrect, energy does not remain the same across the electromagnetic spectrum, and the relationship is inverse, not with energy constant.
• Option C: Incorrect, since \(E\) and \(\lambda\) are inversely proportional, wavelength should decrease as energy increases.
• Option D: Correct, matches the inverse relationship between energy and wavelength.

Answer:

D. Wavelength decreases as energy increases across the electromagnetic spectrum.